Table 2.
Description of the model parameters
| Parameter | sik(x, v) | Description |
|---|---|---|
| Effects associated with variables | ||
| Ego (focal adolescent) | viΣjxij | Main effect of adolescent’s own varname on the selection of friends (sociability) |
| Alter (potential friend) | Σjxijvj | Main effect of potential friends’ varname on the selection of friends (popularity) |
| Ego X alter interaction | viΣjxijv̂j | Expresses the tendency for adolescents with higher values on varname to prefer ties to potential friends who likewise have higher values (this is a form of similarity that increases with distance from the mean) |
| Ego X alter interaction at distance=2 |
viΣjxijv̂j v̂j = alters’ alter v̄ |
Expresses the tendency for adolescents with higher values on varname to prefer ties through an intermediate friend to potential friends who likewise have higher values (this is a form of similarity increasing with distance from the mean reflecting indirect connections). |
| Same varname (adolescent and potential friend)1 | ΣjxijI(vi = vj) | Effect of the adolescent and the potential friend having an identical value on varname |
| Effect paramaterizations | ||
| Evaluation effects | e(x, v) | The baseline effect paramaterization assuming symmetry between the creation and dissolution of friendships |
| Creation effects1 | Δ+c(x, v) | Captures the creation of new ties |
| Endownment/durability effects1 | Δ−d(x, v) | Compares keeping existing ties to dropping them |
| Structural parameters | ||
| Outdegree | Σjxij | General tendency to choose a friend |
| Reciprocity | Σjxijxjl | Tendency to have reciprocal friendships |
| Transitive triplets | Σj,hxihxijxjh | Tendency to become a friend of a friends’ friend (controls for transitive network closure) |
| 3-Cycles2 | Σj,hxijxjhxhi | Tendency for a friend’s friend to chose the adolescent as a friend (generalized reciprocity) |
| Number distance=23 | #(j|xij = 0, G = 2) | Tendency to be indirectly connected through one intermediary (controls for indirect connections) |
I(vi = vj) is a function indicating whether vi = vj (=1) or vi ≠ vj (= 0).
1
Creation and durability operationalizations are included together, thus resulting in two rather than one effect for each parameter included in the model.
2
A positive effect implies generalized reciprocity while a negative effect with a positive transitive triplet effect suggests local hierarchies (Ripley and Snijders 2011).
3
This effect is an inverse effect of network closure so effects tend to be negative, suggesting that indirect connections tend to close or are lost.